Problem: Rewrite as a simplified fraction. ${1.2\overline{8} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 128.8888...\\ 10x &= 12.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 116}$ ${x = \dfrac{116}{90}} $ ${x = \dfrac{58}{45}} \text{or} {1 \dfrac{13}{45}}$